Dominican, I think the reason is purely because NCA are only taking 747 type-rated guys whereas AJX will take non-rated and provide the 767 type rating. Therefore if you joined Eva and already had the type rating on your existing licence (either 747 or A330), you would have less of an issue moving on for a type-rated job as long as you kept the rating current on your ICAO licence with an LPC before you left Eva and at least as often as required to keep it valid on hour ICAO licence e.g. every 3-5 years depending on the licencing authority.
However, I peronally haven't looked into whether it's possible to transfer a type rating from a Taiwanese licence onto my own licence. As previous posters have said, it seems it may be possible, but not on every type of licence.